On the maximal displacement of some critical branching Lévy processes with stable offspring distribution

2025/03/24 by Christophe Profeta, Profeta, Christophe · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2503.18451

openalex publication_date 2025/03/24 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Let X be a critical branching Lévy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different situations: first when the underlying Lévy process L admits moments of order at least two and is not centered, and then when the distribution of L has a regularly varying tail. This work complements some earlier results in which either L was centered or the offspring distribution was assumed to have moments of order three.

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